As attention increasingly focuses on green energy, thermal energy emerges as a widely available energy source. Therefore, harvesting this energy has been the subject of extensive studies. Thermoacoustic-piezoelectric energy harvesters are championed as innovative devices for transferring renewable thermal energy green energy to green energy applications. The onset frequency, a crucial parameter in thermoacoustic engine design and operation, has typically been determined through targeting method or numerical iteration, involving a cumbersome process. This paper introduces an analytical method tailored for one-dimensional standing-wave type thermoacoustic-piezoelectric energy harvesters. The method facilitates the determination of the harvester’s onset frequency under arbitrary boundary conditions. The original thermoacoustic equation is reconstructed by refining the Fourier series, and subsequently yields the eigenvalue equation for the onset frequency through the Galerkin method. Building upon this foundation, the paper explores the impact of factors such as engine length and fluidd type, plate stack length and position, general impedance boundary conditions, and temperature on the onset frequency.